Some of the characters certainly are (well, specisist) but I don't think the show endorses their beliefs. Kira, a resistance fighter, learns that it isn't enough that someone is Cardassian, she got to a place she was able to hate someone for what they did, not who they were, even though she and her people suffered at the hands of a specific group for 50 years. Odo, though he flirts with the Great Link, also never really embraces the Founders' belief that all solids are to be avoided and feared (at worst) and controlled (at best). Sisko's love interest (forget her name at the moment) also reminds him that Vic's racially-integrated 1952 Vegas lounge was not an accurate portrayal of the show circuit at the time, but rather a picture of "the way things could have been, the way they should have been."
Trek as a whole has always pushed for more racial inclusion than the mainstream culture accepted at the time. Nichelle Noris was the first black person on television who wasn't a maid, the first interracial kiss on TV was on TOS, and there were lots of TNG, DS9 and VOY episodes that delt with racism.
I don't think ST can lay claim to the first interracial kiss on TV.
https://en.wikipedia.org/wiki/First_interracial_kiss_on_television